APPENDICES

1. Natural Selection is primarily a theory of the cumulative development of adaptations wherever these occur; and therefore is only incidentally, or likewise, a theory of the origin of species in cases where allied species differ from one another in respect of peculiar characters, which are also adaptive characters.2. Hence, it does not follow from the theory of natural selection that all species—much less all specific characters—must necessarily have owed their origin to natural selection; since it cannot be proved deductively from the theory that no "means of modification" other than natural selection is competent to produce such slight degrees of modification as go to constitute diagnostic distinctions between closely allied species; while, on the other hand, there is an overwhelming mass of evidence to prove the origin of "a large proportional number of specific characters" by causes of modification other than natural selection.3. Therefore, and upon the whole, as Darwin so emphatically held, "Natural selection has been the main, but not the exclusive means of modification."4. Even if it were true that all species and all specific characters must necessarily owe their origin to natural selection, it would still remain illogical to define the theory of natural selection as indifferently a theory of species or a theory of adaptations; for, even upon this erroneous supposition, specific characters and adaptive characters would remain very far indeed from being conterminous—most of the more important adaptations which occur in organic nature being the common property of many species.5. In no case can natural selection have been the cause of mutual infertility between allied, or any other, species—i.e.of the most general of all "specific characters."6. Without Isolation, or the prevention of free intercrossing, organic evolution is in no case possible. Therefore, it is isolation thathasbeen "the exclusive means of modification," or, more correctly, the universal condition to it. Therefore, also, Heredity and Variability being given, the whole theory of organic evolution becomes a theory of the causes and conditions which lead to Isolation.7. Isolation may be either discriminate or indiscriminate. When discriminate, it has reference to resemblances between individuals constituting the isolated colony or group; when indiscriminate, it has no such reference. In the former case there arises Homogamy, and in the latter case there arises Apogamy.8. Except where very large populations are concerned, indiscriminate isolation always tends to become increasingly discriminate; and, in the measure that it does so, apogamy passes into homogamy, by virtue of Independent Variability.9. Natural Selection is one among many other forms of discriminate isolation, and presents in this relation the following peculiarities:—(a) The isolation is with reference to superiority of fitness; (b) is effected by death of the excluded individuals; and (c) unless assisted by some other form of isolation, can only effect monotypic as distinguished from polytypic evolution.10. It is a general law of organic evolution that the number of possible directions in which divergence may occur can never be more than equal to the number of cases of efficient isolation; but, excepting natural selection, any one form of isolation need not necessarily require the co-operationof another form in order to create an additional case of isolation, or to cause polytypic as distinguished from monotypic evolution.11. Where common areas and polytypic evolution are concerned, the most general and most efficient form of isolation has been the physiological, and this whether the mutual infertility has been the antecedent or the consequent of morphological changes on the part of the organisms concerned, and whether or not these changes are of an adaptive character.12. This form of isolation—which, in regard to incipient species, I have called Physiological Selection—may act either alone or in conjunction with other forms of isolation on common areas: in the former case its agency is of most importance among plants and the lower classes of animals; in the latter case its importance consists in its greatly intensifying the segregative power of whatever other form of isolation it may be with which it is associated.

2. Hence, it does not follow from the theory of natural selection that all species—much less all specific characters—must necessarily have owed their origin to natural selection; since it cannot be proved deductively from the theory that no "means of modification" other than natural selection is competent to produce such slight degrees of modification as go to constitute diagnostic distinctions between closely allied species; while, on the other hand, there is an overwhelming mass of evidence to prove the origin of "a large proportional number of specific characters" by causes of modification other than natural selection.

3. Therefore, and upon the whole, as Darwin so emphatically held, "Natural selection has been the main, but not the exclusive means of modification."

4. Even if it were true that all species and all specific characters must necessarily owe their origin to natural selection, it would still remain illogical to define the theory of natural selection as indifferently a theory of species or a theory of adaptations; for, even upon this erroneous supposition, specific characters and adaptive characters would remain very far indeed from being conterminous—most of the more important adaptations which occur in organic nature being the common property of many species.

5. In no case can natural selection have been the cause of mutual infertility between allied, or any other, species—i.e.of the most general of all "specific characters."

6. Without Isolation, or the prevention of free intercrossing, organic evolution is in no case possible. Therefore, it is isolation thathasbeen "the exclusive means of modification," or, more correctly, the universal condition to it. Therefore, also, Heredity and Variability being given, the whole theory of organic evolution becomes a theory of the causes and conditions which lead to Isolation.

7. Isolation may be either discriminate or indiscriminate. When discriminate, it has reference to resemblances between individuals constituting the isolated colony or group; when indiscriminate, it has no such reference. In the former case there arises Homogamy, and in the latter case there arises Apogamy.

8. Except where very large populations are concerned, indiscriminate isolation always tends to become increasingly discriminate; and, in the measure that it does so, apogamy passes into homogamy, by virtue of Independent Variability.

9. Natural Selection is one among many other forms of discriminate isolation, and presents in this relation the following peculiarities:—(a) The isolation is with reference to superiority of fitness; (b) is effected by death of the excluded individuals; and (c) unless assisted by some other form of isolation, can only effect monotypic as distinguished from polytypic evolution.

10. It is a general law of organic evolution that the number of possible directions in which divergence may occur can never be more than equal to the number of cases of efficient isolation; but, excepting natural selection, any one form of isolation need not necessarily require the co-operationof another form in order to create an additional case of isolation, or to cause polytypic as distinguished from monotypic evolution.

11. Where common areas and polytypic evolution are concerned, the most general and most efficient form of isolation has been the physiological, and this whether the mutual infertility has been the antecedent or the consequent of morphological changes on the part of the organisms concerned, and whether or not these changes are of an adaptive character.

12. This form of isolation—which, in regard to incipient species, I have called Physiological Selection—may act either alone or in conjunction with other forms of isolation on common areas: in the former case its agency is of most importance among plants and the lower classes of animals; in the latter case its importance consists in its greatly intensifying the segregative power of whatever other form of isolation it may be with which it is associated.

I have received from Mr. Gulick the results of his consideration of Mr. Wallace's criticism. As these results closely resemble those which I have myself reached, and as they were independently worked out on the other side of the globe, I deem it desirable to publish them here for the sake of comparison.

In his covering letter Mr. Gulick writes:—

Mr. Wallace has most certainly adopted the fundamental principles of our theory, and in an arbitrary way attempted to claim the results produced by these principles as the effects of natural selection. He takes our principles, which in the previous chapter he has combated; but he makes such disjointed use of them that I am not willing to recognize his statement as an intelligible exposition of our theory.... I have endeavoured to indicate at what points Mr. Wallace has deserted his own principles, and at what points he has failed to make the best use of ours. To bring out these points distinctly has been no easy task; but if you regard this paper onThe Preservation and Accumulation of Cross-infertilityas giving any help in elucidating the true principles, and in showing Mr. Wallace's position in regard to them, I shall be satisfied. Please make any use of it that may seem desirable, and then forward it to Professor Dana.

The following is a general summary of Mr. Gulick's results:—

Mr. Wallace's criticism of the theory of Physiological Selection is unsatisfactory; (l) because he has accepted the fundamental principle of that theory on pages 173-9, in that he maintains that without the cross-infertility the incipient species there considered would be swamped; (2) because he assumes that physiological selection pertains simply to the infertility of first crosses, and has nothing to do with the infertility of mongrels and hybrids; (3) because he assumes that infertility between first crosses is of rare occurrence between species of the same genus, ignoring the fact that in many species of plants the pollen of the species is pre-potent on the stigma of the same species when it has to compete with the pollen of other species of the same genus; (4) because he not only ignores Mr. Romanes' statement that cross-infertility often affects "a whole race or strain," but he gratuitously assumes that the theory of Physiological Selection excludes this "racial incompatibility" (which Mr. Romanes maintains is the more probable form), and bases his computation on the assumption that the cross-infertility is not associated with any other form of segregation; (5) because he claims to show that "all infertility not correlated with someusefulvariation has a constant tendency to effect its own elimination," while his computation only shows that, if the cross-infertility is not associated with some form ofpositivesegregation, it will disappear[60]; and (6) because he does not observe that the positive segregation may be secured by the very form of the physiological incompatibility.... Without here entering into any computation, it is evident that, e.g. the prepotency of pollen of each kind with its own kind, if only very slight, will prevent cross-fertilization as effectually as a moderate degree of instinctive preference in the case of an animal.

The paper likewise indicates a point which, in studying Mr. Wallace's theory, I have missed. It will be remembered that the only apparent difference between his theory and mine has been shown to consist in this—that while I was satisfied to state, in a general way, that natural selection is probably able to increase a selective fertility which has already been begun by other causes, Mr. Wallace has sought to exhibit more in detail the precise conditions under which it can do so. Now, Mr. Gulick shows that the particular conditions which Mr. Wallace describes, even if they do serve to promote an increase of cross-infertility, are conditions which preclude the possibility of natural selection coming into play at all. So that if, under these particular conditions, a further increase of cross-infertility does take place, it does not take place in virtue of natural selection. To me it appears that this criticism is sound; and, if so, it disposes of even the one very subordinate addition to our theory which Mr. Wallace "claims" as the most "distinctive" part of his.

The following is the criticism in question:—

On pages 173-186 Mr. Wallace maintains that "Natural selection is, in some probable cases at all events, able to accumulate variations in infertility between incipient species" (p. 174); but his reasoning does not seem to me conclusive. Even if we grant that the increase of this character [cross-infertility] occurs by the steps which he describes,it is not a process of accumulation by natural selection. In order to be a means of cumulative modification of varieties, races, or species, selection, whether artificial or adaptational [i.e. natural], must preserve certain forms of an intergenerating stock, to the exclusion of other forms of the same stock. Progressive change in the size of the occupants of a poultry-yard may be secured by raising only bantams the first, only common fowls the second, and only Shanghai fowls the third year; but this is not the form of selection that has produced the different races of fowls. So in nature, rats may drive out and supplantmice; but this kind of selection modifies neither rats nor mice. On the other hand, if certain variations of mice prevail over others, through their superior success in escaping their pursuers, then modification begins. Now, turning to page 175, we find that, in the illustrative case introduced by Mr. Wallace, the commencement of infertility between the incipient species is in the relations to each other of two portions of a species that are locally segregated from the rest of the species, and partially segregated from each other by different modes of life. These two local varieties, being by the terms of his supposition better adapted to the environment than the freely interbreeding forms in other parts of the general area, increase till they supplant these original forms. Then, in some limited portion of the general area, there arise two still more divergent forms, with greater mutual infertility, and with increased adaptation to the environment, enabling them to prevail throughout the whole area. The process here described, if it takes place, is not modification by natural selection.

On the other hand, itismodification by physiological selection. For, among the several other forms of isolation which are called into requisition, the physiological (i.e. ever accumulating cross-infertility) is supposed to play an important part. That the modification is not modification by natural selection may perhaps be rendered more apparent by observing, that in as far asanyother mode of isolation is involved or supposed, so far is thepossibleagency of natural selection eliminatedas between the two or more otherwise isolated sections of a species; and yet it is modes of isolation other than that furnished by natural selection (i.e. perishing of the less fit), that Mr. Wallace here supposes to have been concerned—including, as I have before shown, the physiological form, to which, indeed, he really assigns most importance of all. Or, as Mr. Gulick states the matter in his independent criticism:—

In the supposed case pictured by Mr. Wallace, the principle by which the two segregating forms are kept from crossing,and so are eventually preserved as permanently distinct forms, is no other than that which Mr. Romanes and myself have discussed under the terms Physiological Selection and Segregate Fecundity. Not only is Mr. Wallace's exposition of the divergence and the continuance of the same in accord with these principles which he has elsewhere rejected, but his whole exposition is at variance with his own principle, which, in the previous chapter, he vigorously maintains in opposition to my statement that many varieties and species of Sandwich Island land molluscs have arisen, while exposed to the same environment, in the isolated groves of the successive valleys of the same mountain range. If he adhered to his own theory, "the greater infertility between the two forms in one portion of the area" would be attributed to a difference between theenvironmentpresented in that portion and that presented in the other portions; and the difficulty would be to consistently show how this greater infertility could continue unabated when the varieties thus characterized spread beyond the environment on which the character depends. But, without power to continue, the process which he describes would not take place. Therefore, in order to solve the problem of theoriginandincreaseof infertility between species, he tacitly gives up his own theory, and adopts not only the theory of Physiological Selection but that of Intensive Segregation[61]through Isolation, though he still insists on calling the process natural selection; for on page 183 he says, "No form of infertility or sterility between the individuals of a species can be increased by natural selection unless correlated with some useful variation, while all infertility not so correlated has a constant tendency to effect its own elimination." Even this claim he seems to unwittingly abandon when on page 184 he says: "The moment it [a species] becomes separated either by geographical or selective isolation, or by diversity of station or of habits, then, while each portion must be kept fertileinter se, there is nothing to prevent infertility arising between the two separated portions."

The criticism proceeds to show yet further inconsistencies and self-contradictions in Mr. Wallace's treatment of this subject; but it now seems needless to continue. Nor, indeed, should I have quoted this much but for the sake of so fully justifying my own criticism by showing the endorsement which it has received from a completely independent examination.

We have seen that the only important point of difference between Mr. Wallace's more recent views and my own on the problem of inter-specific sterility, has reference to the question whether variations in the way of cross-infertility caneverarise and act "alone, in an otherwise undifferentiated species," or whether they canneverso arise and act. It is Mr. Wallace's opinion that, even if they ever do arise alone, at all events they can never act in differentiating a specific type, seeing that the chances against their suitable mating must be so great: only if they be from the first associated with some other form of homogamy, which will have the effect of determining their suitable mating, does he think that they can act in the way supposed by our theory of "selective fertility"[62]. On the other hand, aspreviously and frequently stated, I have so strong a belief in the segregating power of physiological selection, or selective fertility, that I do not think it is necessary for this principle to bealwaysassociated with some other form of homogamy. From the first, indeed, I have laid great stress (as, also, has Mr. Gulick) on the re-enforcing influence which association with any other form of homogamy must exercise upon the physiological form, and vice versa; but I have also said that, in my opinion, the physiological form may in many cases be able to act entirely alone, or without assistance derived from any other source. The question here is, as we have already so fully seen, a question of but secondary importance; since, whether or not the physiological form of homogamy ever acts alone, even Mr. Wallace now allows, or rather argues, that it acts in combination—and this so habitually, as well as with so much effect, that it constitutes a usual condition to the origination of species. Nevertheless, although the only relevancy of his numerical computation of chances—whereby he thinks that he overturns my theoryin toto—is such relevancy as it bears to this question of secondary importance, I have thought it desirable to refer the question, together with Mr. Wallace's views upon it, to the consideration of a trained mathematician.

As this "subordinate question" depends entirely on numerical computations involving the doctrine of chances, I should first of all like to remark, that in reference to biological problems of the kind now before us, I do not myself attach much importance to a merely mathematical analysis. The conditions which such problems involve are so varied and complex, that it is impossible to be sure about the validity of thedataupon which a mathematical analysis isfounded. Nevertheless, for the sake of meeting these criticisms upon their own ground, I will endeavour to show that, even as mathematical calculations, they are quite untrustworthy. And, in order to do this effectually, I will quote the results of a much more competent, as well as a much more thorough, inquiry. I applied to Mr. Moulton for this purpose, not only because he is one of the ablest mathematicians of my acquaintance; but also because his interest in biology, and his knowledge of Darwinian literature, render him well fitted to appreciate exactly, and in all their bearings, the questions which were submitted to his consideration. I need only add that his examination was completely independent, and in no way influenced by me. Having previously read my paper onPhysiological Selection, Mr. Gulick's paper onDivergent Evolution, and Mr. Wallace's book onDarwinism, he was in possession of all the materials; and I merely requested the favour of his opinion upon the whole case from a mathematical point of view. The following is his reply; and I give itin extenso, because it serves to place in another light some of the general considerations which it has already been my endeavour to present[63].

After some introductory remarks on Mr. Wallace's "adoption of the theory of physiological selection pure and simple," and "the pure caricature of it which he puts forward as" mine, the letter proceeds thus:—

The reason why it is so easy to attack your theory is that it is so easy to confuse the survival of anindividualwith thesurvival of apeculiarityoftype. No one has ever said that anindividualisassistedby the possession of selective fertility: that is a matter which cannot affect his chance oflife. Nor has any one said that the possession of selective fertility in anindividualwillof itselfincrease the chance of his havingprogenythat will survive, and in turn become the progenitors of others that will survive. Taken by itself, the fact that anindividualis capable of fertility with some only of the opposite sex lessens the chance of his having progeny. Whether or not he is more or less favourably situated than hisconfreresfor the battle of life must be decided by thetotal sumof his peculiarities; and the question whether or not this selective fertility will be a hindrance must be decided by considerations depending on the other peculiarities associated with it.But when we come to consider the survival or permanence of atypeorpeculiarity, the case is quite different. It then becomes not only a favourable circumstance, but, in my opinion, almost a necessary condition, that the peculiarity should be associated with selective fertility[64].Take the case of the Jews. I don't think that intermarriage with other nations would lessen their fertility, or diminish the number of their progeny; nor is there any reason to think that this progeny would be unequal to the struggle for existence. But no one doubts that the abandonment of their voluntary isolation (which operates so far as this is concerned as a selective fertility), would lead to the disappearance of the familiar Jewish type. All the world would get some of it; but as a whole it would be "swamped."Now although no doubt Wallace would admit all this, he fails to give it the weight it ought to have. In discussing the question of its operation he considers too exclusively the case of the individual.Of course, a type can only be perpetuated through the medium of individuals, and all that his argument amounts to is, thatselective fertility would be so fatal to individuals thatnotype which presents it could be formed or perpetuated—a conclusion which is not only absurd in itself, but contradicted by his own subsequent adoption of your theory. Besides, apart from calculations (with which I will deal when I write next), such reasoning brings its own refutation. Selective fertility is not in the same category as some of the other influences to which an important share has been ascribed in the formation of the existing types.It exists as a recognized phenomenon.Hence all these numerical proofs that it would lead to extinction, because it is so disadvantageous to the possessor, prove too much. They would show that the degree of selective fertility which so frequently characterizes species is a most onerous gift; and that, were it not present, there would be a vastly increased chance of fertility, which would render the races fitter and lead to their increased survival. Why then has it not been got rid of?The two answers which no doubt would be given seem to me to support rather than to make against your theory. In the first place, Wallace might say that this infertility is an advantage because it keeps pure a type which is specially fitted to its surroundings, as shown by its continued existence. But if this be so, and it is necessary to protect thedevelopedtype, how much more necessary to protect theincipienttype! In the second place, he might say that this selective fertility is not so disadvantageous when the species has been formed, because the individual can choose his mate from his like; whereas, when it is beginning to be formed, he must mate blindly, or without what you call "psychological selection." But this seems to me to be wholly inapplicable to at least half the animal, and to all the vegetable kingdom. Moreover, with regard to the other half of the animal kingdom, it merely raises the question,—How soon will such an incipient type recognize itself? Seeing it is probable that many families [broods] will belong to the same [incipient] type, I should not be surprised if it were found that this sexual recognition and preference sets in very early.But this leads me to the question of your letter. I understand you to want me to examine and criticize the attemptednumerical arguments against or for your theory. Now it seems to me that it will be best to take, in the first instance, the vegetable kingdom, and with regard to it I cannot see how there can be any numerical argument against the theory. For we often have species side by side with others nearly allied, but much more numerous. The condition of these is precisely analogous to that of your incipient species. They are exposed to fertilization from, say, ten times as numerous individuals of the allied species. They reject this in favour of that from the relatively few individuals of their own. Yet the two species are in competition. I could go through the numerical arguments of your assailant word for word, applying them to such a case as this, and they would triumphantly show that the specific fertility of the rarer kind would lead to its certain extinction. Yet we know that this is not so.Indeed, the too triumphant character of the logic used against you seems to me to be capable of being turned to your use. If cross-infertility is so intensely disadvantageous to the individuals presenting it, it cannot have beenthatwhich made these individuals and their progeny survive. It is therefore a burden which they have carried. But we find that it is more or less present in all the closely allied types that occur on common areas: therefore it must be a necessary feature in the formation of such types; for it cannot be an accident that it is present in so many. In other words, it must be the price which the individual and his progeny pay for their formation into a type. And this is your theory pure and simple.The more I consider the matter, the more I feel that it is impossible to decide as to the sufficiency of selective fertility to explain the formation of species, if we consider merely the effect it would have on the number of individuals, as contrasted with what it would be if no such peculiarity had developed itself. Indeed, I may say that on pondering over the matter I have come to the conclusion, that mere fertility is probably a comparatively unimportant factor in the preservation of the species, after a certain sufficient degree of fertility is attained. I do not wish to be misunderstood. To a certain point fertility is not only advantageous but necessary, inorder to secure survival of the type; but I feel that little reliance can be placed on calculations based on the numerical co-efficient of fertility (i. e. the ratio of the number of offspring to the number of parents) in determining the relative chance of type-survival.Take, for instance, the oak tree. It produces thousands of acorns, almost the whole of which die without producing any progeny. Have we any reason to believe that if the number of acorns borne by oak trees were diminished, even so much as to one-tenth, the race of oaks would perish? It may of course be said that, if all other things are equal, the probabilities of survival must be increased by increased fertility of this kind; but I feel convinced that when numerical fertility has attained to a high point in circumstances in which actual increase of the race cannot take place to any substantial extent, the numerical value of this fertility sinks down into a factor of the second or third order of importance—that is to say, into the position of a factor whose effects are only to be considered when we have duly allowed for the full effects of all the main factors. Until we have done that, we gain little or nothing in the way of accuracy of conclusion by taking into consideration the minor factors. It may be very well to neglect the effect of the attraction of Jupiter in our early researches on the motion of the Moon; and our doing so will not prevent the results being approximate and having considerable value, because we are retaining the two main factors that establish the motion, viz. the effects of the Earth and the Sun. But if we exclude the effect of one of these main factors, our results would be worthless; and it would not be rendered substantially less so by the fact that we had taken Jupiter into account in arriving at them.You must not imagine, however, that I think it wholly profitless to see whether there would be any substantial effect on numerical fertility wereselectivefertility to manifest itself. But if we want to derive any assistance from calculation, it must be by applying it with a good deal more precision and definiteness than anything that Wallace shows. And, in the first place, it is useless to confuse the vegetable and animal kingdoms. In the former you have union unaffected by choice; in the latter,so far at all events as the higher animals are concerned, you have "psychological selection." In order to give you a specimen of what can safely be done by calculation if you take a problem of sufficient definiteness, I have chosen the case of a flowering plant in which a certain proportion of the race have developed the peculiarity of being sterile with the remainder, while retaining the normal fertility of the race in unions among themselves. In order to give the greatest advantage to your critics, I have assumed that such flowers as possess the peculiarity are not self-fertilizable; for it is clear that if we suppose that they are self-fertilizable, the fertility need be very slightly affected.As I have excluded self-fertilization, it is necessary, if we are to get any trustworthy results, that one should consider the mode in which fertilization will be produced. I have taken the case of fertilization by insects, and have assumed that each flower is visited a certain number of times by insects during the period when fertilization is possible; and, further, that the insects which visit it have on the average visited a certain number of flowers of the same species before they came there. Of course nothing but observation can fix these latter numbers; but I should not be surprised at finding that they are of considerable magnitude[65]. In order to make the results a littlemore intelligible, I have grouped them under the numbers which represent the average number of flowers that an insect visits in a journey. This is a little more than twice as great as the number which represents the number of flowers he has on the average visited before coming to the individual whose fertility we are considering.I send you the formula and the calculation on which it is based in an Appendix; but as I know you have a holy horror of algebraical formulae, I give you here a few numerical results.The cases I have worked out are those in which the number of insects visiting each flower is 5, or 10, or 15; and I have also taken 5, 10, and 15, to represent the number of flowers which an insect visits each journey. This makes nine cases in all; and I have applied these to two instances—viz. one in which one-fifth of the whole race have developed cross-infertility, and the other in which one-tenth only have done so. Taking first the instance where one-fifth have developed the peculiarity, I find that if on the average five insects visit a flower, and each insect on the average visits five flowers on a journey, the fertility is diminished by about one-tenth. If, however, the average number of flowers the insect visits is ten, the reduction of fertility is less than one per cent. And it becomes inappreciable if the average number is fifteen. If on the average ten insects visit each flower, then, if each insect visits on the average five flowers on a journey, the reduction of fertility is a little over one per cent.; but if it visits ten or fifteen the reduction is inappreciable. If fifteen insects visit the flower on an average, then, if these insects on the average visitfive or more flowers on a journey, the reduction of fertility is inappreciable.By the term inappreciable I mean that it is not substantially greater than one-tenth of one per cent.—i.e. not more than one-thousandth.Of course, if the proportion of individuals acquiring the peculiarity is less, the effect on the fertility under the above hypothesis will be greater; and it will not be counteracted so fully unless the number of insect visits is larger, or unless the insects visit more flowers on a journey. Thus if only one-tenth of the race have developed the peculiarity, then, if each flower is visited on the average by five insects who visit five flowers on each trip, the fertility will be reduced about one-third. If, however, the insects visit on the average ten flowers per trip, it will be only diminished about one-tenth; and if they visit fifteen on each trip, it will be only diminished about one-fortieth. If in the same case we suppose that each flower receives ten insect visits, then, if the insects visit on an average five flowers per trip, the fertility will be diminished about one-eighth. If they visit ten on a trip, it will be diminished about one-hundredth, and the diminution is inappreciable if they visit fifteen on a trip. Similarly, if a flower receives fifteen insect visits, the diminution is about one-twenty-fifth, if insects visit on the average five flowers on a trip; and is inappreciable if they visit ten or fifteen.These figures will show you that it is exceedingly possible that a peculiarity like this, the effect of which at first sight would seem to be so prejudicial to fertility, may in fact have little or no influence upon it; and if you set against this the overwhelming importance of such a peculiarity in segregating the type so as to give it a chance of becoming a fixed species, you will, I think, feel that your hypothesis has nothing to fear from a numerical examination.I have not examined the case of fertilization by other means; nor have I examined the case of fertilization in animals, where psychological selection can come in. To obtain any useful results, one would have to consider very carefully the circumstances of each case; and at present, at all events, I do not think it would be useful to do so. Nor have I attempted toshow the converse of the problem—viz. the effect of swamping where cross-fertilization is possible. I shall be very glad to examine any one of these cases if you want me to do so; but I should prefer to leave it until I hear from you again.If you contrast the results that I have given above with those given on pages 181 to 183 of Wallace's book, you will see the enormous difference. His calculations can only apply to the animal kingdom in those cases in which there is only a union between one individual of each sex; and before you can deal with the question of such animals, you will have to take into consideration many elements besides that of mere fertility, if you wish to get any tolerably accurate result[66].

But when we come to consider the survival or permanence of atypeorpeculiarity, the case is quite different. It then becomes not only a favourable circumstance, but, in my opinion, almost a necessary condition, that the peculiarity should be associated with selective fertility[64].

Take the case of the Jews. I don't think that intermarriage with other nations would lessen their fertility, or diminish the number of their progeny; nor is there any reason to think that this progeny would be unequal to the struggle for existence. But no one doubts that the abandonment of their voluntary isolation (which operates so far as this is concerned as a selective fertility), would lead to the disappearance of the familiar Jewish type. All the world would get some of it; but as a whole it would be "swamped."

Now although no doubt Wallace would admit all this, he fails to give it the weight it ought to have. In discussing the question of its operation he considers too exclusively the case of the individual.

Of course, a type can only be perpetuated through the medium of individuals, and all that his argument amounts to is, thatselective fertility would be so fatal to individuals thatnotype which presents it could be formed or perpetuated—a conclusion which is not only absurd in itself, but contradicted by his own subsequent adoption of your theory. Besides, apart from calculations (with which I will deal when I write next), such reasoning brings its own refutation. Selective fertility is not in the same category as some of the other influences to which an important share has been ascribed in the formation of the existing types.It exists as a recognized phenomenon.Hence all these numerical proofs that it would lead to extinction, because it is so disadvantageous to the possessor, prove too much. They would show that the degree of selective fertility which so frequently characterizes species is a most onerous gift; and that, were it not present, there would be a vastly increased chance of fertility, which would render the races fitter and lead to their increased survival. Why then has it not been got rid of?

The two answers which no doubt would be given seem to me to support rather than to make against your theory. In the first place, Wallace might say that this infertility is an advantage because it keeps pure a type which is specially fitted to its surroundings, as shown by its continued existence. But if this be so, and it is necessary to protect thedevelopedtype, how much more necessary to protect theincipienttype! In the second place, he might say that this selective fertility is not so disadvantageous when the species has been formed, because the individual can choose his mate from his like; whereas, when it is beginning to be formed, he must mate blindly, or without what you call "psychological selection." But this seems to me to be wholly inapplicable to at least half the animal, and to all the vegetable kingdom. Moreover, with regard to the other half of the animal kingdom, it merely raises the question,—How soon will such an incipient type recognize itself? Seeing it is probable that many families [broods] will belong to the same [incipient] type, I should not be surprised if it were found that this sexual recognition and preference sets in very early.

But this leads me to the question of your letter. I understand you to want me to examine and criticize the attemptednumerical arguments against or for your theory. Now it seems to me that it will be best to take, in the first instance, the vegetable kingdom, and with regard to it I cannot see how there can be any numerical argument against the theory. For we often have species side by side with others nearly allied, but much more numerous. The condition of these is precisely analogous to that of your incipient species. They are exposed to fertilization from, say, ten times as numerous individuals of the allied species. They reject this in favour of that from the relatively few individuals of their own. Yet the two species are in competition. I could go through the numerical arguments of your assailant word for word, applying them to such a case as this, and they would triumphantly show that the specific fertility of the rarer kind would lead to its certain extinction. Yet we know that this is not so.

Indeed, the too triumphant character of the logic used against you seems to me to be capable of being turned to your use. If cross-infertility is so intensely disadvantageous to the individuals presenting it, it cannot have beenthatwhich made these individuals and their progeny survive. It is therefore a burden which they have carried. But we find that it is more or less present in all the closely allied types that occur on common areas: therefore it must be a necessary feature in the formation of such types; for it cannot be an accident that it is present in so many. In other words, it must be the price which the individual and his progeny pay for their formation into a type. And this is your theory pure and simple.

The more I consider the matter, the more I feel that it is impossible to decide as to the sufficiency of selective fertility to explain the formation of species, if we consider merely the effect it would have on the number of individuals, as contrasted with what it would be if no such peculiarity had developed itself. Indeed, I may say that on pondering over the matter I have come to the conclusion, that mere fertility is probably a comparatively unimportant factor in the preservation of the species, after a certain sufficient degree of fertility is attained. I do not wish to be misunderstood. To a certain point fertility is not only advantageous but necessary, inorder to secure survival of the type; but I feel that little reliance can be placed on calculations based on the numerical co-efficient of fertility (i. e. the ratio of the number of offspring to the number of parents) in determining the relative chance of type-survival.

Take, for instance, the oak tree. It produces thousands of acorns, almost the whole of which die without producing any progeny. Have we any reason to believe that if the number of acorns borne by oak trees were diminished, even so much as to one-tenth, the race of oaks would perish? It may of course be said that, if all other things are equal, the probabilities of survival must be increased by increased fertility of this kind; but I feel convinced that when numerical fertility has attained to a high point in circumstances in which actual increase of the race cannot take place to any substantial extent, the numerical value of this fertility sinks down into a factor of the second or third order of importance—that is to say, into the position of a factor whose effects are only to be considered when we have duly allowed for the full effects of all the main factors. Until we have done that, we gain little or nothing in the way of accuracy of conclusion by taking into consideration the minor factors. It may be very well to neglect the effect of the attraction of Jupiter in our early researches on the motion of the Moon; and our doing so will not prevent the results being approximate and having considerable value, because we are retaining the two main factors that establish the motion, viz. the effects of the Earth and the Sun. But if we exclude the effect of one of these main factors, our results would be worthless; and it would not be rendered substantially less so by the fact that we had taken Jupiter into account in arriving at them.

You must not imagine, however, that I think it wholly profitless to see whether there would be any substantial effect on numerical fertility wereselectivefertility to manifest itself. But if we want to derive any assistance from calculation, it must be by applying it with a good deal more precision and definiteness than anything that Wallace shows. And, in the first place, it is useless to confuse the vegetable and animal kingdoms. In the former you have union unaffected by choice; in the latter,so far at all events as the higher animals are concerned, you have "psychological selection." In order to give you a specimen of what can safely be done by calculation if you take a problem of sufficient definiteness, I have chosen the case of a flowering plant in which a certain proportion of the race have developed the peculiarity of being sterile with the remainder, while retaining the normal fertility of the race in unions among themselves. In order to give the greatest advantage to your critics, I have assumed that such flowers as possess the peculiarity are not self-fertilizable; for it is clear that if we suppose that they are self-fertilizable, the fertility need be very slightly affected.

As I have excluded self-fertilization, it is necessary, if we are to get any trustworthy results, that one should consider the mode in which fertilization will be produced. I have taken the case of fertilization by insects, and have assumed that each flower is visited a certain number of times by insects during the period when fertilization is possible; and, further, that the insects which visit it have on the average visited a certain number of flowers of the same species before they came there. Of course nothing but observation can fix these latter numbers; but I should not be surprised at finding that they are of considerable magnitude[65]. In order to make the results a littlemore intelligible, I have grouped them under the numbers which represent the average number of flowers that an insect visits in a journey. This is a little more than twice as great as the number which represents the number of flowers he has on the average visited before coming to the individual whose fertility we are considering.

I send you the formula and the calculation on which it is based in an Appendix; but as I know you have a holy horror of algebraical formulae, I give you here a few numerical results.

The cases I have worked out are those in which the number of insects visiting each flower is 5, or 10, or 15; and I have also taken 5, 10, and 15, to represent the number of flowers which an insect visits each journey. This makes nine cases in all; and I have applied these to two instances—viz. one in which one-fifth of the whole race have developed cross-infertility, and the other in which one-tenth only have done so. Taking first the instance where one-fifth have developed the peculiarity, I find that if on the average five insects visit a flower, and each insect on the average visits five flowers on a journey, the fertility is diminished by about one-tenth. If, however, the average number of flowers the insect visits is ten, the reduction of fertility is less than one per cent. And it becomes inappreciable if the average number is fifteen. If on the average ten insects visit each flower, then, if each insect visits on the average five flowers on a journey, the reduction of fertility is a little over one per cent.; but if it visits ten or fifteen the reduction is inappreciable. If fifteen insects visit the flower on an average, then, if these insects on the average visitfive or more flowers on a journey, the reduction of fertility is inappreciable.

By the term inappreciable I mean that it is not substantially greater than one-tenth of one per cent.—i.e. not more than one-thousandth.

Of course, if the proportion of individuals acquiring the peculiarity is less, the effect on the fertility under the above hypothesis will be greater; and it will not be counteracted so fully unless the number of insect visits is larger, or unless the insects visit more flowers on a journey. Thus if only one-tenth of the race have developed the peculiarity, then, if each flower is visited on the average by five insects who visit five flowers on each trip, the fertility will be reduced about one-third. If, however, the insects visit on the average ten flowers per trip, it will be only diminished about one-tenth; and if they visit fifteen on each trip, it will be only diminished about one-fortieth. If in the same case we suppose that each flower receives ten insect visits, then, if the insects visit on an average five flowers per trip, the fertility will be diminished about one-eighth. If they visit ten on a trip, it will be diminished about one-hundredth, and the diminution is inappreciable if they visit fifteen on a trip. Similarly, if a flower receives fifteen insect visits, the diminution is about one-twenty-fifth, if insects visit on the average five flowers on a trip; and is inappreciable if they visit ten or fifteen.

These figures will show you that it is exceedingly possible that a peculiarity like this, the effect of which at first sight would seem to be so prejudicial to fertility, may in fact have little or no influence upon it; and if you set against this the overwhelming importance of such a peculiarity in segregating the type so as to give it a chance of becoming a fixed species, you will, I think, feel that your hypothesis has nothing to fear from a numerical examination.

I have not examined the case of fertilization by other means; nor have I examined the case of fertilization in animals, where psychological selection can come in. To obtain any useful results, one would have to consider very carefully the circumstances of each case; and at present, at all events, I do not think it would be useful to do so. Nor have I attempted toshow the converse of the problem—viz. the effect of swamping where cross-fertilization is possible. I shall be very glad to examine any one of these cases if you want me to do so; but I should prefer to leave it until I hear from you again.

If you contrast the results that I have given above with those given on pages 181 to 183 of Wallace's book, you will see the enormous difference. His calculations can only apply to the animal kingdom in those cases in which there is only a union between one individual of each sex; and before you can deal with the question of such animals, you will have to take into consideration many elements besides that of mere fertility, if you wish to get any tolerably accurate result[66].

The above analysis leaves nothing to be added by me. But, in conclusion, I may once more repeat that the particular point with which it is concerned is a point of very subordinate importance. For even if Mr. Wallace's computation of chances had been found by Mr. Moulton to have been an adequate computation—and, therefore, even if it had been thus proved that physiological homogamy must always be associated with some other form of homogamy in order to produce specific divergence—still the importance of selective fertility as a factor of organic evolution would not have been at all diminished. For such a result would merely have shown that, not only "in many cases" (as I originally said), but actually in all cases, the selective fertility which I hold to have been so generally concerned in the differentiation of species has required for this purpose the co-operation of some among the numerous other forms of homogamy. But inasmuch as, by hypothesis, no one of these other or co-operating factors would of itself have been capable of effecting specific divergence in any of the cases where its association with selective fertility is concerned, the mathematicalproof that such an association isalways—and not merelyoften—necessary, would not have materially affected the theory of the origin of species by means of physiological selection. We have now seen, however, that a competent mathematical treatment proves the exact opposite; and, therefore, that Mr. Wallace's criticism fails even as regards the very subordinate point in question.

Bearing of Weismannism on Physiological Selection.—If in view of other considerations I could fully accept Professor Weismann's theory of heredity, it would appear to me in no small measure to strengthen my own theory of physiological selection. For Weismann's theory supposes that all changes of specific type must have their origin in variations of a continuous germ-plasm. Butthe more the origin of species is referred directly to variations arising in the sexual elements, the greater is the play given to the principles of physiological selection[67]; while, on the other hand, the less standing-ground is furnished to the theory that cross-infertility between allied species is due to "external conditions of life," "prolonged exposure to uniform change of conditions," "structural modifications re-acting on the sexual functions"; or, in short, that "somatogenetic" changes of any kind can of themselves induce the "blastogenetic" change of cross-infertility between progeny of the same parental stock.

Cross-infertility and Diversity of Life.—Observe that one great consequence of duly recognizing the importance of intercrossing is indefinitely to raise our estimate of the part played by the principle of cross-infertility in diversifying organic nature. For whenever in any line of descent the bar ofsterility arises, there the condition is given for a new crop of departures (species of a genus); and when genera are formed by the occurrence of this bar, there natural selection and all other equilibrating causes are supplied with new material for carrying on adaptational changes in new directions. Thus, owing to cross-infertility, all these causes are enabled to work out numberless adaptations in many directions (i. e. lines of descent) simultaneously.

Cross-infertility and Stability.—The importance of sterility as a diagnostic feature is obvious if we consider that more than any other feature it serves to givestabilityto the type; and unless a type is stable or constant, it cannot be ranked as a species. That Darwin himself attributes the highest importance to this feature as diagnostic, seeForms of Flowers, pp. 58, 64.

Cross-infertility and Specific Differentiation.—In their elaborate work on the many species of the genus Hieracium, Nägeli and Peter are led to the general conclusion that the best defined species are always those which display absolute sterilityinter se; while the species which present most difficulty to the systematist are always those which most easily hybridize. Moreover, they find, as another general rule applicable to the whole genus, that there is a constant correlation between inability to hybridize and absence of intermediate varieties, and, conversely, between ability to hybridize and the presence of such varieties.

Cross-infertility in Domesticated Cattle.—Mr. J. W. Crompton, who has had a large experience as a professional cattle-breeder, writes to me (March 2, 1887)—

"That form of barrenness, very common in some districts, which makes heifers become what are called 'bullers'—that is, irregularly in 'season,' wild, and failing to conceive—is certainly produced by excess of iron in their drinking-water, and I suspect also by a deficiency of potash in the soil."

He also informs me that pure white beasts of either sex are so well known by experienced breeders to be comparatively infertile together, that they are never used for breeding purposes, so that "in some parts of the country, where a tendency to sterility had become so confirmed in the white race that they utterly died out," only the coloured breeds are now to be found. He goes on to say that if "a lot of white heifers were put to a lot of white bulls, I think you would probably get a fertile breed of pure white cattle.... I think, in short, that domestication has produced just what your theory suggests, a new variety inclined to prove sterile with its parent stock."

Commenting on the origin of domesticated cattle, Professor Oscar Schmidt remarks (Doctrine of Descent, p. 139)—

"Rütimeyer's minute researches on domestic cattle have shown that, in Europe at least, three well-defined species of the diluvial period have contributed to their formation—Bos primigenius,longifrons, andfrontosus. These species once lived geographically separate, but contemporaneously; and they and their specific peculiarities have perished, to rise again in our domestic races. These races breed together with unqualified fertility. In the form of skull and horns they recall one or other of the extinct species; but collectively they constitute a new main species. That from their various breeds, the three or any one of the aboriginal species would ever emerge in a state of pristine purity, would be an utterly ludicrous assertion."

Now, seeing that these "aboriginal species," although living "contemporaneously," were "geographically separate," we can well understand that their divergence of type from a common ancestor did not require, as a condition to their divergence, that any cross-sterility should have arisen between them. The geographical isolation was enough to secure immunity from mutual intercrossing, and therefore, as our present theory would have expected as probable, morphological divergence occurred without any corresponding physiologicaldivergence, as must almost certainly have been the case if such polytypic evolution had occurred on a common area. Indeed, one of the two lines of experimental verification of our theory consists in selecting cases where nearly allied species are separated by geographical barriers, and proving that, in such cases, there is no cross-sterility.

Fertility of Domesticated Varieties.—Some writers have sought to explain the contrast between domesticated varieties and natural species in respect of fertility when crossed, by the consideration that it is only those natural species which have proved themselves so far flexible as to continue fertile under changed conditions of life that can have ever allowed themselves to become domesticated. But although this condition may well serve to explain the unimpaired fertility under domestication of such species as for this very reason have ever become domesticated, I fail to see how it explains the further and altogether different fact, that this fertility continues unimpaired between all the newly differentiated morphological types which have been derived from the original specific type. It is one thing that this type should continue fertile after domestication: it is quite another thing that fertility should continue as between all its modified descendants, even although the amount of modification may extend much further than that which usually obtains between different natural species.

Testing for Cross-infertilityamong varieties growing on the same area is a much more crucial line of verification than testing for unimpaired fertility between allied species which occupy different areas, because while in the former case we are dealing with "incipient species" with a view to ascertaining whether the divergence which they have already undergone is accompanied by physiological isolation, in the latter case we can never be sure that two allied species, which are now widely disconnected geographically, have always been sodisconnected. They may both have originated on the same area; or one may have diverged from the other before it migrated from that area; or even if, when it migrated, it was unchanged, and if in its new home it afterwards split into two species by physiological selection, the newer species would probably prove infertile, not only with its parent type, but also with its grand-parent in any other part of the world.

Seebohm on Isolation.—Seebohm is so strongly influenced by the difficulty from "the swamping effects of free intercrossing," that he is driven by it to adopt Asa Gray's hypothesis of variations as teleological. Indeed, he goes as far as Wagner, for he maintains that in no case can there be divergence or multiplication of species without isolation. He makes the important statement that "the more the geographical distribution of birds is studied, the more doubtful it seems to be that any species of bird has ever been differentiated without the aid of geographical isolation" (Charadriidae, p. 17). If this is true, it makes in favour of physiological selection by showing the paramount importance of the swamping effects of intercrossing, and consequent importance of isolation. But it makes against physiological selection by showing that the geographical form of isolation is sufficient to explain all the cases of specific differentiation in birds. But I must remember that the latter point rests largely on negative inference, and that birds, owing to their highly locomotive habits, are the class of animals where physiological selection is likely to be most handicapped.

Herbert on Hybridization.—Herbert tells us that when he first astonished the Horticultural Society by laying before them the results of his experiments on hybridization, his brother botanists took serious alarm. For it appeared to them that this "intermixture of species would confuse the labours of botanists, and force them to work their way through a wilderness of uncertainty." Therefore he was bluntly toldby several of these gentlemen, "I do not thank you for your mules." Now, although naturalists have travelled far and learnt much since those days, it appears to me that a modern evolutionist might still turn to the horticulturist with the same words. For assuredly he has no reason to thank the horticulturist for his mules, until he has found a satisfactory answer to the question why it is that natural species differ so profoundly as regards their capacity for hybridizing.

Advance on Herbert's Position.—- If it be said that all my work amounts to showing what Herbert said long ago—viz. that the only true or natural distinction between organic types is the sexual distinction—I answer that my work does much more than this. For it shows that the principle of sterility is the main condition to the differentiation, not merely of species and genera, but also to the evolution of adaptations everywhere, in higher as well as in lower taxonomic divisions. Moreover, even though naturalists were everywhere to consent to abandon specific designations, and, as Herbert advises, to "entrench themselves behind genera," there would still remain the facts of what are now called specific differences (of the secondary or morphological kind), and by whatever name these are called, they alike demand explanation at the hands of the evolutionist.

Fritz Müller on Cross-infertility.—Fritz Müller writes, "Every plant requires, for the production of the strongest possible and most prolific progeny, a certain amount of difference between male and female elements which unite. Fertility is diminished as well when this degree is too low (in relatives too closely allied) as when it is too high (in those too little related)." Then he adds, as a general rule, "Species which are wholly sterile with pollen of the same stock, and even with pollen of nearly allied stocks, will generally be fertilized very readily by the pollen of another species. The self-sterile species of the genus Abutilon,which are, on the other hand, so much inclined to hybridization, afford a good example of this theory, which appears to be confirmed also by Lobelia, Passiflora, and Oncidium" (American Naturalist, vol. viii, pp. 223-4, 1874).

Different groups of plants exhibit remarkable differences in the capability of their constituent species to hybridize.—In so far as these differences have reference only to first crosses, they have no bearing either for or against my theory. Only in so far as the differences extend to the production of fertile hybrids does any question arise for me. First of all, therefore, I must ascertain whether (or how far) there is any correlation between groups whose species manifest aptitude to form first crosses, and groups where first crosses manifest aptitude to produce fertile hybrids. Next, whatever the result of this inquiry should be, if I find that certain natural groups of plants exhibit comparatively well-marked tendencies to form fertile hybrids, the question will arise, Are these tendencies correlated withpaucityof species? If they are, the fact would make strongly in favour of physiological selection. For the fact would mean that in these natural groups, owing to "the nature of the organisms" included under them, less opportunity is given to physiological selection in its work of differentiating specific types than is given by other natural groups where the nature of the organism renders them more prone to mutual sterility. But in prosecuting this branch of verification, I must remember to allow for possibilities of differential degrees of geographical isolation in the different groups compared.

On this subject Focke writes me as follows:—"In a natural group (family, order, genus) showing considerable variability in the structure of the flower, we may expect to find [or do find] a greater number of mules than in a group whose species are only distinguished by differences in the shape of the leaves, or in growth, &c. I do notknow, however, which in this connexion of things is the cause and which the effect. A useful ancestral structure of the flower may be conserved by an otherwise varying progeny, on condition that the progress of diversity be not disturbed by frequent intercrossings. [Therefore, if this condition be satisfied, the structure of the flower in different members of the group will continue constant: here the cause ofconstancyin the flower (however much variability there may be in the leaves, &c.) is its originalinabilityto hybridize.] On the other hand, in species or groups ready to hybridize [or capable of hybridizing], the fixation of a new specific type will require some change in the structure of the flower, and a change considerable enough to alter the conditions of fertilization. [Here the reason of theinconstancy of the flower in different members of the group is the originalaptitudeof their ancestral forms to hybridize.] Perhaps there is something in this suggestion, but certainly there are other efficient physiological relations, which are at present unknown. Your theory of physiological selection may serve to explain many difficult facts."

The Importance of Prepotency.—A. Kerner shows by means of his own observations on sundry species of plants which hybridize in the wild state, that they do so very much more frequently if both, or even if only one of the parent forms be rare in the neighbourhood. This fact can only be explained by supposing that, even in species most prone to hybridizing under Nature, there is some degree of prepotency of pollen of the same species over that of the other species; so that where both species are common, it is correspondingly rare that the foreign pollen gets a chance. But if there were no prepotency, the two species would blend; and this Kerner supposes must actually take place wherever two previously separated species, thus physiologically circumstanced, happen to be brought together. (Kerner's paper is published inOester. Bot. Zeitschrift, XXI, 1871, where he alludes to sundry other papers of his own advocating similar views.)

The relation of these observations to Jordan'sespèces affinesis obvious. We have only to suppose that some such slight and constant difference characterizes the sexual elements of these allied varieties as demonstrably characterizes their morphology, and we can understand how pollen-prepotency would keep the forms distinct—such forms, therefore, being so many records of such prepotency.

Both from Kerner's work, and still more from that of Jordan and Nägeli, I conclude that (at all events in plants) prepotency is the way in which physiological selection chiefly acts. That is to say,suddenandextremevariations in the way of sexual incompatibility are probably rare, as compared with some degree of prepotency. According as this degree is small or great so will be the amount of the corresponding separation. This view would show that in plants the principle of physiological selection is one of immensely widespread influence, causing (on the same areas) more or less permanent varieties much below specific rank. And when we remember on how delicate a balance of physiological conditions complete correspondency of pollen to ovules depends, we may be prepared to expect that the phenomenon of prepotency is not of uncommon occurrence.

Self-fertilization and Variability.—It occurred to Count Berg Sagnitz that, if physiological selection is a true principle in nature, vegetable species in which self-fertilization obtains ought to be more rich in constant varieties than are species in which cross-fertilization rules. For, although even in the latter case physiological isolation may occasionally arise, it cannot be of such habitual or constant occurrence as it must be in the former case. Acting on this idea, Count Berg Sagnitz applied himself to ascertain whether there is any general correlation between thehabit of self-fertilization and the fact of high variability; and he says that in all the cases which he has hitherto investigated, the correlation in question is unmistakable.

Additional Hypothesis concerning Physiological Selection.—In reciprocal crossesA×Bis often more fertile thanB×A. If hybridABis more fertile withA, and hybridBAwithB, than vice versa, there would be given a good analogy on which to found the following hypothesis.

LetAandBbe two intergenerating groups in which segregate fecundity is first beginning. Of the hybrids,ABwill be more fertile withA, andBAwithB, than vice versa. The interbreeding ofABwithAwill eventually modify sexual characters ofAby assimilating it to those ofAB, while the interbreeding ofBAwithBwill similarly modify sexual characters ofBby assimilating it to those ofBA. Consequently,Awill become more and more infertile withB, whileBbecomes more and more infertile withA. Fewer and fewer hybrids will thus be produced till mutual sterility is complete.

To sustain this hypothesis it would be needful to prove experimentally, (1) that hybrid formsABare more fertile withAthan withB, while hybrid formsBAare more fertile withBthan withA[or, it may be possible that the opposite relations would be found to obtain, viz. thatABwould be more fertile withB, andBAwithA]; (2) that, if so, effect of intercrossingABwithAis to make progeny more fertile withAthan withB, while effect of intercrossingBAwithBis to make progeny more fertile withBthan withA.

Such experiments had best be tried with species where there is already known to be a difference of fertility between reciprocal crosses (e.g. Matthiola annua and M. glabra, seeOrigin of Species, p. 244).

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